AdvAlg2Ch6

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Use this link for the following sections:

In Class Textbook pages 344 to 381




Advanced Algebra II – Chapter 6 – Polynomial Functions

Section 1 – Polynomial Functions:
  • Define Polynomial Function
  • Find degree and leading coefficient
  • Understand what a polynomial in one variable is
  • Evaluate a polynomial function at a numerical value
  • Evaluate a polynomial function with a variable value
  • Be able to describe end behavior of a polynomial function
  • Be able to tell how many real zeros a polynomial function has from the graph
  • Know how to do examples 1-4 in the book, read them and copy into notes

Section 2 – Graphing Polynomial Functions:
  • Make a table of values and graph a polynomial function
    • Plug in at least 10 points
    • If the graph turns, plug in decimal values to try and find the exact turning point (min or max)
    • Approximate zeros of the functions by looking for sign changes in the table of values

  • Know when the graph is changing directions or hitting a zero. Plug in extra values as needed
  • Know how to do examples 1-3 in the book. Read them and copy into notes

Section 3 – Solving Polynomial Equations:
  • Review the Zero Product Property
  • Be able to factor fully any polynomial
    • Sum/Difference of cubes
    • Quadratic Form
    • Grouping
  • Apply the zero product property after the polynomial is factored and solve the equation

Section 4 – The Remainder Theorem, Factor Theorem:
  • Evaluate functions using synthetic division
  • Apply the remainder theorem to evaluate functions
  • Divide a known factor out of a polynomial and factor what remains



Section 5 – Roots and Zeros:

  • Determine how many roots and what type you will have in a polynomial
  • Find all of the roots of a polynomial equation
  • Know how to find conjugate pairs of imaginary and irrational roots
  • Write a polynomial equation in factored form and standard form when given the root

Section 6 – Rational Root Theorem:
  • If there are no known factors, Apply the Rational Root Theorem
    • List all of the possible rational roots
    • Test them with synthetic division
    • Once you find what works, factor what remains

Extra Topics
  • Finding intervals of Increase and Decrease
  • Using Multiplicity to determine sketches of graphs



Homework:
  • Section 1 p350 16-44 even
  • Section 2 p356 14-26 even
  • Section 3 p363 17-24, 29-30 all
  • Section 4 p368 14-30 even
  • Section 5 p375 35-41, Normal Textbook p333 29-31
  • Section 6 p381 12-32 even